Hello World! An Invitation to Computer Science

Lecture Slides

Functions in Python
Monday April 7, 2008

Key ideas from last time

• interpreters v. compilers
• Python designed for ease of use, readability
• case sensitivity of identifiers
• basic datatypes and expressions
• simple examples

Functions

• function definitions v. function calls
• another source of non-linear control flow
• abstraction: hiding details (and potential complexity)
    provides readability
    can save lots of space - avoids repetition
    make changes, fix errors only once
  

Function input

• formal parameters v. actual arguments
• arguments can be arbitrary expressions
• argument names independent from parameter names
• parameter names act as local variables

Function output

• return values more general than "print"
• output often designed to be input to another function
    rather than for human reader
• common for one function to call another

Incremental development

top-down approach

example: generate list of prime numbers

• overview:

      for each number n up to limit
         if n is prime then print n
  

• testing a number is prime:

    while we have not found a factor 
              and we have not gone past square root
      if number is divisible by i
         then factor has been found
       otherwise increase i by 1
  

• divisibility & square-root comparison